Tensor-Based Morphometry (TBM) is an increasingly popular method for group analysis of brain MRI and DTI data. The main steps in the analysis consist of a nonlinear registration to align each individual scan to a common space, and a subsequent statistical analysis to determine morphometric differences, or difference in fiber structure between groups. Here, we propose a method to improve both the nonlinear registration and statistical analyses for TBM. The traditional nonlinear registration for TBM is performed on T1-weighted MR images, either on the seg- mented 2D cortices alone, or on the whole 3D brain images, followed by corresponding statistical analyses on those domains. To date, neither option provides a satisfactory solution for the entire brain, since 2D cortical TBM ignores the rest of the brain, while 3D volumetric TBM has difficulty matching the cortex and may not match well neuronal fiber structures in the white matter. Here we describe a new statistical nonlinear registration algorithm for 3D volumetric TBM that combines the advantages of cortical matching to those of a 3D statistical fluid registration on the whole brain volume. In addition, we aim to match the underlying fiber structure accurately by adding a distance between diffusion tensors in the cost function derived from diffusion tensor imaging data. Furthermore, we propose to improve the detection power in the statistical analysis in TBM by using all the information available in the Jacobian of the deformation field in a multivariate fashion, and by setting up the inference so that it can be interpreted in terms of both volumetric changes and directions of deformation. PUBLIC HEALTH RELEVANCE: We improve on Tensor-Based Morphometry for group analysis in two ways, first by using cortical, structural MR and DTI information into a combined cortical and statistical fluid registration algorithm, and secondly by using multivariate statistical methods to analyze the full Jacobian matrix and the volumetric and directional information in it.